A395633 - OEIS

%I #6 May 11 2026 19:00:04

%S 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,2,3,2,3,2,3,2,3,2,3,3,4,3,4,3,5,3,5,

%T 3,5,4,5,3,6,3,5,4,5,3,7,4,6,5,6,4,8,4,7,5,7,4,9,4,7,6,7,4,10,4,7,6,8,

%U 5,10,5,9,7,8,5,12,5,9,7,10,5,11,6,10

%N a(n) = number of triples (x, y, z) such that 2*x^2 + y*z = n, where x, y, z are positive integers satisfying y < x < z.

%e a(28) = 3 counts these triples: (2, 1, 20), (3, 1, 10), (3, 2, 5).

%t t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - 2 x^2 <= 0, {},

%t Map[({x, #, Quotient[n - 2 x^2, #]} &),

%t Select[Divisors[n - 2 x^2], Divisible[n - 2 x^2, #] &]]],

%t {x, 1, Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];

%t c = (#2 < #1 < #3 &);

%t Table[Length[t[n, c]], {n, 11, 130}]

%t (* _Peter J. C. Moses_, Mar 29 2026 *)

%Y Cf. A393710, A394038, A394788, A395632.

%K nonn

%O 11,12

%A _Clark Kimberling_, May 02 2026